Ed Miliband said there was 'a gulf miles wide between the kind of politics that people want and what prime minister’s questions offers'. Photograph: PA

Ed Miliband has proposed a weekly "public question time" where an audience would be allowed to tackle the prime minister on any issue of the day.

In a radical suggestion for changing the culture of politics, the Labour leader will write to the speaker of the House of Commons with more details of his idea about how to make the prime minister more directly accountable to the people.

Labour said the audience for the public Q&A should be representative of the country and that it should be held in parliament at least fortnightly, but ideally weekly.

While Downing Street said David Cameron was open to new ways of engaging with the public, it also noted that he already holds "PM Direct" sessions where he took questions from people in towns and cities across the country.

However, these sessions, about once a month, are not always carried on television and are usually held with employees in their places of work, meaning people have to ask questions in a formal context in front of their bosses.

Ed Miliband is shown an image of Wallace on the Andrew Marr Show. Photograph: Handout/Getty Images

Speaking on the BBC's Andrew Marr Show on Sunday morning, Miliband said there needed to be a session "where regularly the prime minister submits himself or herself to questioning from members of the public in the Palace of Westminster on Wednesdays".

He said: "We'll see how often we do it. We definitely want to do it regularly and I want to make a formal proposal to the Speaker of the House of Commons. He and I talked before many times about prime minister's questions.

"Let me put it this way: at the moment there's a few inches of glass that separates the public in the gallery from the House of Commons but there's a gulf miles wide between the kind of politics that people want and what prime minister's questions offers."

Senior politicians, including Miliband and Cameron, have criticised prime minister's questions, held in the chamber every Wednesday, for being too aggressive and combative.

The Speaker, John Bercow, has repeatedly called for an end to the "orchestrated barracking" and claimed several female MPs avoid the sessions because of the atmosphere. Despite his entreaties PMQs has continued in the same vein.

Miliband said his proposal for public involvement was not a gimmick. It comes after he made a speech on Friday about his personal political style, saying he was not a politician out of "central casting", in contrast with Cameron's courting of photo opportunities and repetition of soundbites. "I want to find ways to change our political culture," he said. "It's not just about putting the photo-op first. That is a problem, but it is deep, this, and it goes beyond that."

Miliband said that Nick Clegg, the deputy prime minister, was right to do a weekly radio phone-in with members of the public and he would try to do something similar. "I know at the time he got a whole lot of bile about it when he did it and I remember saying to people, actually, it's a good thing to do. I want to do that and I will do that in terms of radio phone-ins, but I want to do something more."

Bercow's office said it would examine any proposals submitted by the Labour leader, which it said echoed ideas already submitted to a review he is undertaking into the future of politics.

"The Speaker will look at Mr Miliband's suggestions with interest, when he receives them. Clearly, any changes would be a matter for the House," his spokeswoman said.

"The Speaker's special commission looking at the effects of the digital revolution on our democracy has received similar suggestions from people outside parliament.

"However, it is clear that within Westminster there is also an appetite for further reforms to the way the House of Commons conducts itself."